1.3.1. A model of language

The idea of truth conditions or a proposition suggests a simple picture of the way language works. According to this picture, each sentence has truth conditions that are determined by the semantic rules of the language. These truth conditions settle the truth value of the sentence in each possible world, something that is encapsulated in a proposition. The proposition expressed by a sentence is its meaning. The meaning of an expression smaller than a sentence is to be found in the contribution this expression makes to the propositions expressed by sentences containing it. And, from this point of view, the function of language is to convey propositions.

Just as the information content of a sentence is to be found by considering the range of possible worlds it rules out, the information that a person possesses is to be found by considering the possible worlds that he or she is able to rule out. The more I can rule out, the more information I have; and the kind of information I have is determined by the particular worlds I can rule out. This means that the sum total of my knowledge can be thought of as a proposition.

Our aim in acquiring information could be described as an attempt to distinguish the actual state of the world among the various alternative possibilities—in short, to locate the actual world within the space of all possible worlds. The proposition representing our knowledge goes some distance towards in ruling out some possibilities. But it will leave many open, and the actual world could be any of those open possibilities. If someone conveys a proposition to us, we are able to rule out a whole region of logical space, a region that can be added to the region ruled out by our existing knowledge. And, in general, this will reduce our uncertainty about the location in logical space of the actual world.

We can generate information to give to others by delimiting a region within the total area we know to be ruled out. Ideally, perhaps, we would simply convey the whole of what we know; but language limits our ability to do this since only a limited range of propositions are expressed by reasonably short sentences. To convey information, we select a sentence that is entailed by what we know and assert it, thereby conveying the proposition it expresses.

This is process is illustrated in the following artificial example of sharing information.

>

|<

φ

ψ

χ

θ

>|

Fig. 1.3.1-1. An animation of a conversation in which information is shared. The button > will play the full conversation while the buttons φ, ψ, χ, and θ will each play one of its four stages. The buttons |< and >| move to the initial and final state, respectively.

Initially, the person on the left is able to rule out regions at the left and right of logical space as possibilities for the actual world while the person on the right is able to rule out regions at the top and bottom. The animation then shows a conversation in which each party in turn notices the truth of the one the sentences φ, ψ, χ, and θ and asserts it. The other person accepts this assertion as true and adds its content to the region ruled out by his or her beliefs. At the end of the conversation, the two people share the ability to rule out a region around the boundary of logical space though they still differ in the shape of the region left open in the middle.

In this conversation, each party is depicted as accepting what the other says as true and adding to his or her own beliefs. The person accepting the assertion could be said to modify his or her beliefs in a way that makes it something he or she might assert. This is an example of a process that the philosopher David Lewis labeled accommodation. In this case of accommodation, one’s beliefs are altered to accommodate an assertion someone else has made.

Of course, we do not always accept what others say—i.e., we do not always alter our beliefs to accommodate their assertions—for we may doubt that they are sincere or that they know what they are talking about. But this cannot be the ordinary case. Words can acquire and maintain a conventional meaning only if people usually mean what they say. And assertion could not have the significance it does unless people were usually willing to accept assertions as well-founded. A critical attitude is important; but, at least practically, it must be the exception. Even when we are critical and ask for the grounds of someone's assertion, our request can be met only if we are at some point willing to accept assertions providing grounds as well-founded; and, when we are willing, this will rarely be because there is no room for further doubt. In short, while we do not always accommodate what others say, accommodation is central to the aspects of language this model captures. And, we will see that other forms of accommodation are essential to a number of the aspects of language this model does not capture.

There is one simplification in the picture above that is not an essential feature of the model it depicts but is worth mentioning because it concerns an important use of entailment. Entailment already appears in one way by setting bounds on the range of sentences that we can sincerely assert: if what we assert is to be something we believe, it must be entailed by our beliefs. But entailment also plays a role in our acceptance of what is asserted to us. Even when we do not doubt what has been asserted, we often add only some of its content to our beliefs. While, ideally, we might like to add the full content of what we hear to our beliefs, our ability to store information is limited, and what we do store is determined by our interests. And, if what we store is to be really part of what was asserted it must be implied by that assertion. That is, a fuller picture of the way a proposition is conveyed is the following:

The first entailment arrow marks one aspect of the process of determining what to assert (invention in the terminology of traditional rhetoric) while the second marks one aspect of the process of interpretation.